Author: L. Bostock
Publisher: Nelson Thornes
Release Date: 1984
Dealing with mechanics and the solving of mechanical problems with the help of pure mathematics, this A-Level text introduces at an early stage an appreciation of the properties of vectors. Throughout the book problems are solved using vector methods where appropriate, and many worked examples are provided to illustrate each main development of a topic. A set of straightforward problems follows each section, and a selection of more challenging questions appears in the miscellaneous exercises at the end of most chapters, with multiple-choice questions on most topics.
Many students who embark on a GCE A-level course in mathematics choose the combination of pure mathematics with applications to mechanics. This book provides the mechanics element of such a course. It also contains a section on probability, a topic included in many A-level mathematics syllabuses.
Quantum probability is a subtle blend of quantum mechanics and classical probability theory. Its important ideas can be traced to the pioneering work of Richard Feynman in his path integral formalism. Only recently have the concept and ideas of quantum probability been presented in a rigorous axiomatic framework, and this book provides a coherent and comprehensive exposition of this approach. It gives a unified treatment of operational statistics, generalized measure theory and the path integral formalism that can only be found in scattered research articles. The first two chapters survey the necessary background in quantum mechanics and probability theory and therefore the book is fairly self-contained, assuming only an elementary knowledge of linear operators in Hilbert space.
Author: Richard von Mises
Publisher: Academic Press
Release Date: 2013-09-03
Studies in Mathematics and Mechanics is a collection of studies presented to Professor Richard von Mises as a token of reverence and appreciation on the occasion of his seventieth birthday which occurred on April 19, 1953. von Mises’ thought has been a stimulus in many seemingly unconnected fields of mathematics, science, and philosophy, to which he has contributed decisive results and new formulations of fundamental concepts. The book contains 42 chapters organized into five parts. Part I contains papers on algebra, number theory and geometry. These include a study of Poincaré’s representation of a hyperbolic space on an Euclidean half-space and elementary estimates for the least primitive root. Part II on analysis includes papers on a generalization of Green's Formula and its application to the Cauchy problem for a hyperbolic equation, and the fundamental solutions of a singular Beltrami operator. Part III deals with theoretical mechanics and covers topics such as turbulent flow, axially symmetric flow, and oscillating wakes. The papers in Part IV focus on applied mechanics. These include studies on plastic flow under high stresses and the problem of inelastic thermal stresses. Part V presents studies on probability and statistics, including a finite frequency theory of probability and the problem of expansion of clusters of galaxies.
Author: John du Feu
Publisher: Hachette UK
Release Date: 2018-05-29
Genre: Study Aids
Endorsed by Cambridge Assessment International Education to provide full support for Paper 4 of the syllabus for examination from 2020. Take mathematical understanding to the next level with this accessible series, written by experienced authors, examiners and teachers. - Improve confidence as a mathematician with clear explanations, worked examples, diverse activities and engaging discussion points. - Advance problem-solving, interpretation and communication skills through a wealth of questions that promote higher-order thinking. - Prepare for further study or life beyond the classroom by applying mathematics to other subjects and modelling real-world situations. - Reinforce learning with opportunities for digital practice via links to the Mathematics in Education and Industry's (MEI) Integral platform in the eTextbooks.* *To have full access to the eTextbooks and Integral resources you must be subscribed to both Dynamic Learning and Integral. To trial our eTextbooks and/or subscribe to Dynamic Learning, visit: www.hoddereducation.co.uk/dynamic-learning; to view samples of the Integral resources and/or subscribe to Integral, visit www.integralmaths.org. This book covers the syllabus content for Further Probability and Statistics, including continuous random variables, inference using normal and t-distributions, chi-squared tests, non-parametric tests and probability generating functions. About the series: Four separate textbooks ensure full coverage of the latest Cambridge International AS & A Level Further Mathematics syllabus (9231). Student and Whiteboard eTextbook editions are also available. Further Pure Mathematics 1: Student Textbook (ISBN 9781510421783), Student eTextbook (ISBN 9781510422025), Whiteboard eTextbook (ISBN 9781510422032) Further Pure Mathematics 2: Student Textbook (ISBN 9781510421790), Student eTextbook (ISBN 9781510422063), Whiteboard eTextbook (ISBN 9781510422070) Further Mechanics: Student Textbook (ISBN 9781510421806), Student eTextbook (ISBN 9781510422100), Whiteboard eTextbook (ISBN 9781510422117) Further Probability & Statistics: Student Textbook (ISBN 9781510421813), Student eTextbook (ISBN 9781510422148), Whiteboard eTextbook (ISBN 9781510422155)
Axiomatics of Classical Statistical Mechanics provides an understanding of classical statistical mechanics as a deductive system. This book presents the mechanical systems of a finite number of degrees of freedom. Organized into seven chapters, this book begins with an overview of the average behavior of mechanical systems. This text then examines the concept of a mechanical system and explains the equations of motion of the system. Other chapters consider an ensemble of mechanical systems wherein a Hamiltonian function and a truncated canonical probability density corresponds to each system. This book discusses as well the necessary and sufficient conditions that are given for the existence of statistically stationary states and for the approach of mechanical systems towards these states. The final chapter deals with the fundamental laws of thermodynamics. This book is a valuable resource for mathematicians.
New Tertiary Mathematics, Volume 2, Part 2: Further Applied Mathematics deals with various topics of theoretical mechanics and probability, from statics and the dynamics of a rigid body to the dynamics of a particle with one and two degrees of freedom. Many examples of varying difficulty are worked in the text and exercises are added after each major topic is covered. This book is comprised of five chapters and opens with a discussion on statics, with particular reference to the analysis of systems of forces in three dimensions, along with virtual work, stability, and the catenary. Complicated equilibrium problems are considered. The reader is then introduced to the dynamics of a particle in one and two dimensions, as well as the implications of the Galilean transformation and the general theorems of motion for a system of particles. These theorems are applied to simple cases of the motion of a rigid body. The final chapter on probability examines normal and Poisson distributions, Markov chains, and miscellaneous problems. This monograph will be a useful resource for mathematical pupils and students engaged in private study.
Author: Mark Levi
Publisher: Princeton University Press
Release Date: 2012
In this delightful book, Levi turns math and physics upside down, revealing how physics can simplify proofs and lead to quicker solutions and new theorems, and how physical solutions can illustrate why results are true in ways lengthy mathematical calculations never can.
Assuming GCSE as a starting point (National Curriculum Level 7/8), this A-Level mathematics text provides transitional material in the early chapters for students from a variety of mathematical backgrounds, and caters for a wide spread of ability. It contains the core for A-Level mathematics as outlined in all examination board syllabuses, and additional coverage is included to cater for the pure maths content of A-Level mathematics courses combining pure maths with mechanics / statistics / decision (discrete) maths, and the first half of A-Level pure mathematics.
This series has been developed specifically for the Cambridge International AS & A Level Mathematics (9709) syllabus to be examined from 2020. Cambridge International AS & A Level Mathematics: Probability & Statistics 2 matches the corresponding unit of the syllabus, with a clear and logical progression through. It contains materials on topics such as hypothesis testing, Poisson distribution, linear combinations and continuous random variables, and sampling. This coursebook contains a variety of features including recap sections for students to check their prior knowledge, detailed explanations and worked examples, end-of-chapter and cross-topic review exercises and 'Explore' tasks to encourage deeper thinking around mathematical concepts. Answers to coursebook questions are at the back of the book.
Author: Linda Bostock
Publisher: Nelson Thornes
Release Date: 2000
Genre: Juvenile Nonfiction
Since the launch of the Human Genome project in 1990, understanding molecular and clinical genetics has become an essential aspect of modern medical education. Solid knowledge of genetics is now crucial to a host of healthcare professionals including primary care physicians, nurses and physician assistants. This third edition takes this crucial information and incorporates it into a student-friendly format that focuses on the core concept of human genetics. Each chapter uses the same problem-based approach as the previous editions, and addresses the important role of genetics and disease by integrating molecular and clinical genetics.
Inequalities and Extremal Problems in Probability and Statistics: Selected Topics presents various kinds of useful inequalities that are applicable in many areas of mathematics, the sciences, and engineering. The book enables the reader to grasp the importance of inequalities and how they relate to probability and statistics. This will be an extremely useful book for researchers and graduate students in probability, statistics, and econometrics, as well as specialists working across sciences, engineering, financial mathematics, insurance, and mathematical modeling of large risks. Teaches users how to understand useful inequalities Applicable across mathematics, sciences, and engineering Presented by a team of leading experts